Thin films are layers of material(s) deposited on a surface of another material, such as paper. Thin films are an essential component in many products. Common examples include thin film coatings of silicone on paper for use as a release coating for adhesive labels and silicone films that line diapers and other hygiene products to repel moisture as a method of keeping skin dry. Films used in these products typically range from less than a nanometer (10 Å) to several hundred micrometers in thickness. They can be formed by many different processes, including spin coating, vacuum evaporation, sputtering, vapor deposition, and dip coating. To perform their desired functions, thin films must have the appropriate thickness, composition, and other important characteristics. These properties must be precisely monitored both during and after fabrication.
The thickness of thin films is typically measured by stylus based or optical techniques. Stylus techniques measure thickness by monitoring the deflections of a fine-tipped stylus as it is dragged along the surface of the film. Stylus instruments, which may actually damage the films being measured, are limited in speed and accuracy. Optical techniques, which measure film thickness by measuring film interaction with light, are nondestructive and more accurate. Optical techniques are also usually preferred because they require little or no sample preparation.
One optical technique works by measuring the relative amount of light absorbed by a sample in two or more wavelength bands of the infrared (IR) spectrum. In the simplest case, two bands are used, a measure band and a reference band. The measure band is selected to coincide with a strong absorption in the target material (film to be measured), and the reference band is selected to match a weakly absorbing region of the target material. In more complicated cases, the measure band for one target may be the reference band for another target.
The transmission measurement is based on Beer's Law, which states I=I0e−μw, where I0 is the signal with no sample, I is the signal with sample, μ is the absorption coefficient, and w is the weight of the sample. Equivalently, this may be written as w=(1/μ) ln(I0/I). Thus for a given wavelength of IR radiation, the weight, or thickness of the film, is proportional to the logarithm of the attenuation.
In practice the accuracy of such transmission techniques is limited when measuring in the thin film regime due to an interference fringing effect. Fringes in the transmission spectrum of the measured film appear due to interference of the light reflected from the film surfaces with light transmitted through the film. An example is illustrated in FIG. 1, which shows interference fringes 31 forming when the transmission of a 16 μm polyamide film is measured at different wavelengths. As a result the sensor calibration error for such films increases significantly making measurements inaccurate. The lower limit is about 15–30 microns for IR radiation, and depends on the material of the film.
To understand the fringing effect, consider a thin film with thickness d and index of refraction n, deposited on another material as shown in FIG. 2. Both the top and bottom of the film will reflect a portion of the incident light. The total amount of reflected light is the sum of these two reflections. Because of the wavelike nature of light, the reflections from the two interfaces may add together constructively or destructively, depending on their phase relationship. Their phase relationship is determined by the difference in the optical path lengths of the two reflections, which in turn is determined by the thickness of the film, d. Reflections are in-phase and therefore add constructively when the light path is equal to one integral multiple of the wavelength of light. For light perpendicularly incident on a film, this occurs when 2nd=iλ, where d is the thickness of the film, i is an integer, and λ is the free space wavelength of the incident radiation. (The factor of two accounts for the fact that the light passes through two interfaces.) Conversely, reflections are out of phase and add destructively when the light path is half of a wavelength different from the in-phase condition, or when 2nd=(i+½)λ.
The qualitative aspects of these reflections may be combined in a single equation:R=A+B cos(2πnd/λ).
From this we see that the reflectance will vary periodically with wave number 1/λ Furthermore, at a given wavelength (index of refraction n is wavelength dependent) the frequency of oscillations is proportional to film thickness d. The light that is not reflected, that is, the transmitted light, can be detected by sensors located on the opposite side of the film. It will have a similar periodic component superposed on a non-oscillatory signal.
Because the spectral position and intensity of the fringes depend on the film thickness, it is possible to extend current transmission sensors into the thin film regime by measuring the shape of the fringes and extracting the film thickness from the fringe parameters.